Submission #426328

#	Time	Username	Problem	Language	Result	Execution time	Memory
426328		timmyfeng	Shortcut (IOI16_shortcut)	C++17	0 / 100	1 ms	332 KiB

shortcut

#include <bits/stdc++.h>
using namespace std;

const int N = 1000001;

long long fenw[N][2], sum[N], diff[N], x[N];
int sum_order[N], diff_order[N], n;

array<long long, 2> query(int a) {
    long long min_ans = LLONG_MAX, max_ans = LLONG_MIN;
    for ( ; a > 0; a -= a & -a) {
        min_ans = min(min_ans, fenw[a][0]);
        max_ans = max(max_ans, fenw[a][1]);
    }
    return {min_ans, max_ans};
}

void update(int a, long long x, long long y) {
    for ( ; a <= n; a += a & -a) {
        fenw[a][0] = min(fenw[a][0], x);
        fenw[a][1] = max(fenw[a][1], y);
    }
}

long long find_shortcut(int n, vector<int> l, vector<int> d, int c) {
    // for all (i, j) where i < j: if (x_j + d_j) - (x_i - d_i) > k,
    //      -k + c + (x_j + d_j) + (x_i + d_i) <= s + t <= k - c + (x_j - d_j) + (x_i - d_i)
    //      -k + c + (x_j + d_j) - (x_i - d_i) <= t - s <= k - c + (x_j - d_j) - (x_i + d_i)

    //  for each j, find the max{x_i + d_i} and the min{x_i - d_i}

    ::n = n;

    for (int i = 0; i < n - 1; ++i) {
        x[i + 1] = x[i] + l[i];
    }

    for (int i = 0; i < n; ++i) {
        sum[i] = x[i] + d[i];
        diff[i] = x[i] - d[i];
    }

    iota(sum_order, sum_order + n, 0);
    sort(sum_order, sum_order + n, [&](int a, int b) {
        return sum[a] < sum[b];
    });

    iota(diff_order, diff_order + n, 0);
    sort(diff_order, diff_order + n, [&](int a, int b) {
        return diff[a] < diff[b];
    });

    long long low = 0, high = sum[sum_order[n - 1]] - diff[diff_order[0]];
    while (low < high) {
        long long mid = (low + high) / 2;

        long long min_sum = LLONG_MIN, max_sum = LLONG_MAX;
        long long min_diff = LLONG_MIN, max_diff = LLONG_MAX;

        /*
        for (int i = 0; i < n; ++i) {
            fenw[i][0] = LLONG_MAX;
            fenw[i][1] = LLONG_MIN;
        }

        for (int i = 0, j = 0; j < n; ++j) {
            while (i < n && sum[sum_order[j]] - diff[diff_order[i]] > mid) {
                update(diff_order[i] + 1, diff[diff_order[i]], sum[diff_order[i]]);
                ++i;
            }

            auto [min_i, max_i] = query(sum_order[j]);
            if (min_i < LLONG_MAX) {
                min_sum = max(min_sum, -mid + c + sum[sum_order[j]] + max_i);
                max_sum = min(max_sum, mid - c + diff[sum_order[j]] + min_i);
                min_diff = max(min_diff, -mid + c + sum[sum_order[j]] - min_i);
                max_diff = min(max_diff, mid - c + diff[sum_order[j]] - max_i);
            }
        }
        */

        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < n; ++j) {
                if (sum[j] - diff[i] > mid) {
                    min_sum = max(min_sum, -mid + c + sum[j] + sum[i]);
                    max_sum = min(max_sum, mid - c + diff[j] + diff[i]);
                    min_diff = max(min_diff, -mid + c + sum[j] - diff[i]);
                    max_diff = min(max_diff, mid - c + diff[j] - sum[i]);
                }
            }
        }

        bool ok = false;
        int l1 = n - 1, l2 = 0, r1 = n - 1, r2 = 0;
        for (int i = 0; i < n; ++i) {
            while (l1 >= 0 && x[i] + x[l1] >= min_sum) {
                --l1;
            }
            while (r1 >= 0 && x[i] + x[r1] > max_sum) {
                --r1;
            }
            while (l2 < n && x[i] - x[l2] > max_diff) {
                ++l2;
            }
            while (r2 < n && x[i] - x[r2] >= min_diff) {
                ++r2;
            }
            ok |= max(l1 + 1, l2) < min(r1 + 1, r2);
        }

        if (ok) {
            high = mid;
        } else {
            low = mid + 1;
        }
    }

    return low;
}

• Subtask 1: 0 / 9
• Subtask 2: 0 / 14
• Subtask 3: 0 / 8
• Subtask 4: 0 / 7
• Subtask 5: 0 / 33
• Subtask 6: 0 / 22
• Subtask 7: 0 / 4
• Subtask 8: 0 / 3